The one-person helicopter doesn't have quite the cachet of the jetpack, but it has its own futuristic appeal. There's its appearance in the dystopian future of Road Warrior, of course. And more than one mid-20th-century imagining of the future included personal helicopters or gyrocopters as part of the skyscape. Apparently, the military was thinking along the same lines: here, from 1960, is the U.S. Navy's Gyrodyne YRON-1 Rotorcycle.
Alas, the navy abandoned the project shortly after this ad, for the gas turbine that powered it, was published. Feasibility probably accounts for the dearth of personal helicopters clogging today's sky, though there are some nifty models out there—if you've got tens of thousands of dollars to spend.